Rule to form Le Subjonctif Présent

Question

If you say the stem has to be the stem of the infinitive, then yes, you'll find lots of irregular verbs. But there's a much better rule, and I'd say the few verbs that don't follow it could be called irregular in the Subjonctif Présent.

- je/tu/il/elle/on/ils/elles: the stem is the Indicatif Présent third person plural, minus -ent

- nous/vous: the stem is the Indicatif Présent second/third first plural, minus -ons

Examples:

aimer -> ils aiment -> aim-

venir -> ils viennent -> vienn-

tenir -> ils tiennent -> tienn-

prendre -> ils prennent -> prenn-

...

There are not that many exceptions to this rule. Some important ones:

- avoir -> aie/aies/ait/ayons/ayez/aient
- être -> soi- (turns into soyons/soyez making ii into y)
- faire -> fass-
- pouvoir -> puiss-
- savoir -> sach-
- aller -> aill- / all-
- valoir -> vaill- / val-
- vouloir -> veuill- / voul-

NOTE: where there are two stems, the second one is for nous/vous, the first one is for all others.

Answer

The rule for forming the subjunctive present is just that: take the stem of the third person plural in present tense and add the corresponding subjunctive suffixes.

I agree with you, that they are not really irregular in the way they form the subjunctive. They only are irregular in forming the 3rd person plural, but that's a different matter.